#include <bits/stdc++.h>
#define ll long long
#define debug if (0)
const int MAX_N = 5e5;
const ll MOD = 1e9 + 7;
ll a[MAX_N + 3];
ll b[MAX_N + 3];
int n, q;
ll pref_sum[MAX_N + 3];
int next_2_mul[MAX_N + 3];
// for the segment tree
const ll BASE = 1 << 19;
std::pair<ll, ll> tree[2 * BASE + 5];
void insert(int i, int lo, int hi, int v, ll ap, ll bp) {
if (i < lo || i > hi || lo > hi)
return;
if (lo == hi) {
tree[v] = {ap, bp};
return;
}
int mid = (lo + hi) / 2;
if (i <= mid)
insert(i, lo, mid, v * 2, ap, bp);
else
insert(i, mid + 1, hi, v * 2 + 1, ap, bp);
tree[v] = {
(tree[v * 2 + 1].first * tree[v * 2].first) % MOD,
(tree[v * 2 + 1].first * tree[v * 2].second + tree[v * 2 + 1].second) %
MOD};
}
std::pair<ll, ll> query(int L, int R, int lo, int hi, int v) {
if (L > R || lo > hi || R < lo || L > hi)
return {1, 0};
if (lo >= L && hi <= R) {
return tree[v];
}
int mid = (lo + hi) / 2;
auto [a1, b1] = query(L, R, lo, mid, v * 2);
auto [a2, b2] = query(L, R, mid + 1, hi, v * 2 + 1);
return {(a2 * a1) % MOD, (a2 * b1 + b2) % MOD};
}
void preprocess() {
// pref_sum
pref_sum[0] = 0;
for (int i = 1; i <= n; i++)
pref_sum[i] = pref_sum[i - 1] + b[i];
// next_2_mul
int last_2_mul = -1;
for (int i = n; i >= 1; i--) {
if (a[i] >= 2)
last_2_mul = i;
next_2_mul[i] = last_2_mul;
}
// build the tree
for (int i = 1; i <= n; i++)
if (a[i] == 1)
insert(i, 1, n, 1, 1, b[i]);
else
insert(i, 1, n, 1, a[i], 0);
}
// NOT modulo!
ll sum(int l, int r) {
if (l > r)
return 0;
return pref_sum[r] - pref_sum[l - 1];
}
ll query(ll x, int l, int r) {
int ROUNDS = 32;
int i = l + 1;
bool above_max = false;
for (int round = 1; round <= ROUNDS;
round++) { // after one round, result should be twice as large
if (i > r)
break;
// add until next mul by >= 2
int j = next_2_mul[i];
if (j == -1 || j > r) {
// just adding till the end
x = (x + sum(i, r)) % MOD;
i = r + 1;
break;
} else {
x += sum(i, j - 1);
i = j;
if (x >= MOD) {
above_max = true;
break;
}
}
// add or multiply
assert(a[i] >= 2);
if (above_max || x * a[i] >= x + b[i])
x = (x * a[i]) % MOD;
else
x = (x + b[i]) % MOD;
i++;
}
x %= MOD;
// in the end, apply optimal suffix, if anything is left
if (i <= r) {
auto [ap, bp] = query(i, r, 1, n, 1);
x = (ap * x + bp) % MOD;
}
return x;
}
int main() {
std::ios_base::sync_with_stdio(0);
std::cin.tie(NULL);
std::cin >> n >> q;
for (int i = 1; i <= n; i++)
std::cin >> b[i] >> a[i];
preprocess();
while (q--) {
ll x, l, r;
std::cin >> x >> l >> r;
std::cout << query(x, l, r) << "\n";
}
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 | #include <bits/stdc++.h> #define ll long long #define debug if (0) const int MAX_N = 5e5; const ll MOD = 1e9 + 7; ll a[MAX_N + 3]; ll b[MAX_N + 3]; int n, q; ll pref_sum[MAX_N + 3]; int next_2_mul[MAX_N + 3]; // for the segment tree const ll BASE = 1 << 19; std::pair<ll, ll> tree[2 * BASE + 5]; void insert(int i, int lo, int hi, int v, ll ap, ll bp) { if (i < lo || i > hi || lo > hi) return; if (lo == hi) { tree[v] = {ap, bp}; return; } int mid = (lo + hi) / 2; if (i <= mid) insert(i, lo, mid, v * 2, ap, bp); else insert(i, mid + 1, hi, v * 2 + 1, ap, bp); tree[v] = { (tree[v * 2 + 1].first * tree[v * 2].first) % MOD, (tree[v * 2 + 1].first * tree[v * 2].second + tree[v * 2 + 1].second) % MOD}; } std::pair<ll, ll> query(int L, int R, int lo, int hi, int v) { if (L > R || lo > hi || R < lo || L > hi) return {1, 0}; if (lo >= L && hi <= R) { return tree[v]; } int mid = (lo + hi) / 2; auto [a1, b1] = query(L, R, lo, mid, v * 2); auto [a2, b2] = query(L, R, mid + 1, hi, v * 2 + 1); return {(a2 * a1) % MOD, (a2 * b1 + b2) % MOD}; } void preprocess() { // pref_sum pref_sum[0] = 0; for (int i = 1; i <= n; i++) pref_sum[i] = pref_sum[i - 1] + b[i]; // next_2_mul int last_2_mul = -1; for (int i = n; i >= 1; i--) { if (a[i] >= 2) last_2_mul = i; next_2_mul[i] = last_2_mul; } // build the tree for (int i = 1; i <= n; i++) if (a[i] == 1) insert(i, 1, n, 1, 1, b[i]); else insert(i, 1, n, 1, a[i], 0); } // NOT modulo! ll sum(int l, int r) { if (l > r) return 0; return pref_sum[r] - pref_sum[l - 1]; } ll query(ll x, int l, int r) { int ROUNDS = 32; int i = l + 1; bool above_max = false; for (int round = 1; round <= ROUNDS; round++) { // after one round, result should be twice as large if (i > r) break; // add until next mul by >= 2 int j = next_2_mul[i]; if (j == -1 || j > r) { // just adding till the end x = (x + sum(i, r)) % MOD; i = r + 1; break; } else { x += sum(i, j - 1); i = j; if (x >= MOD) { above_max = true; break; } } // add or multiply assert(a[i] >= 2); if (above_max || x * a[i] >= x + b[i]) x = (x * a[i]) % MOD; else x = (x + b[i]) % MOD; i++; } x %= MOD; // in the end, apply optimal suffix, if anything is left if (i <= r) { auto [ap, bp] = query(i, r, 1, n, 1); x = (ap * x + bp) % MOD; } return x; } int main() { std::ios_base::sync_with_stdio(0); std::cin.tie(NULL); std::cin >> n >> q; for (int i = 1; i <= n; i++) std::cin >> b[i] >> a[i]; preprocess(); while (q--) { ll x, l, r; std::cin >> x >> l >> r; std::cout << query(x, l, r) << "\n"; } } |
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